A pharmacy and a bank, 500 m apart, are situated between Emma's house and Gwen's house. The bank is halfway between the two houses and the pharmacy is closer to Gwen's house. Emma and Gwen left their homes at the same time and arrived at the pharmacy at the same time. Emma drove at a speed of 61 km/h while Gwen drove at a speed 20 km/h slower than Emma. Leaving your answer in kilometres,

1. how much farther did Emma travel than Gwen?
2. how far is Gwen's house from the bank?

(a)
Let the distance between Emma's house and Gwen's house be 1 d.
Gwen travelled = ¹₂ d - 500 m
Emma travelled = ¹₂ d + 500 m

Distance that Emma travelled more than Gwen
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Emma took to travel to the pharmacy
= 1 ÷ 20
= ¹₂₀ h

Distance that Emma travelled
= ¹₂₀ x 61
= 3.05 km

1000 m = 1 km
500 m = 0.5 km

Distance between Gwen's house and the bank
= 3.05 - 0.5
= 2.55 km

Answer(s): (a) 1 km; (b) 2.55 km